Factorization results with combinatorial proofs.
Factorization theorems for strong maps between matroids of arbitrary cardinality
In this paper we present factorization theorems for strong maps between matroids of arbitrary cardinality. Moreover, we present a new way to prove the factorization theorem for strong maps between finite matroids.
Factorizations and Paige's theorem on complete maps.
Factorizations of properties of graphs
A property of graphs is any isomorphism closed class of simple graphs. For given properties of graphs ₁,₂,...,ₙ a vertex (₁, ₂, ...,ₙ)-partition of a graph G is a partition V₁,V₂,...,Vₙ of V(G) such that for each i = 1,2,...,n the induced subgraph has property . The class of all graphs having a vertex (₁, ₂, ...,ₙ)-partition is denoted by ₁∘₂∘...∘ₙ. A property is said to be reducible with respect to a lattice of properties of graphs if there are n ≥ 2 properties ₁,₂,...,ₙ ∈ such that = ₁∘₂∘...∘ₙ;...
Factors and circuits in -free graphs
Factors of alternating sums of products of binomial and q-binomial coefficients
Factors of claw-free graphs
Factors of sums of powers of binomial coefficients
Fair majorities in proportional voting
In parliaments elected by proportional systems the seats are allocated to the elected political parties roughly proportionally to the shares of votes for the party lists. Assuming that members of the parliament representing the same party are voting together, it has sense to require that distribution of the influence of the parties in parliamentary decision making is proportional to the distribution of seats. There exist measures (so called voting power indices) reflecting an ability of each party...
Faithful enclosing of triple systems: Doubling the index.
Fall coloring of graphs I
A fall coloring of a graph G is a proper coloring of the vertex set of G such that every vertex of G is a color dominating vertex in G (that is, it has at least one neighbor in each of the other color classes). The fall coloring number of G is the minimum size of a fall color partition of G (when it exists). Trivially, for any graph G, . In this paper, we show the existence of an infinite family of graphs G with prescribed values for χ(G) and . We also obtain the smallest non-fall colorable...
Falling factorials, generating functions, and conjoint ranking tables.
Families of -symplectic metrics on full flag manifolds.
Families of strongly projective graphs
We give several characterisations of strongly projective graphs which generalise in many respects odd cycles and complete graphs [7]. We prove that all known families of projective graphs contain only strongly projective graphs, including complete graphs, odd cycles, Kneser graphs and non-bipartite distance-transitive graphs of diameter d ≥ 3.
Families of triples with high minimum degree are hamiltonian
In this paper we show that every family of triples, that is, a 3-uniform hypergraph, with minimum degree at least [...] contains a tight Hamiltonian cycle
Fans and bundles in the graph of pairwise sums and products.
Fast approximation of centrality.
Fast Fourier analysis for over a finite field and related numerical experiments.
Faster algorithms for Frobenius numbers.
Faster backtracking algorithms for the generation of symmetry-invariant permutations.